Interactive Physics

In class yesterday, I had mentioned a program called Interactive Physics. The program functions like a "construction kit" for basic Newtonian mechanics. It has a very nice, intuitive interface for setting-up simulations. Once the simulation is started you can see the movement of the objects in real-time. You can also have the program dynamically display velocity or acceleration vectors for the objects in the simulation. These quantities can also be plotted in a graph. And you can obtain a free demo of this fantastic software!

I have been using the demo version of this program to experiment with the models presented in a book on acoustics by Aurthor Benade. In his Fundamentals of Acoustics, Benade presents a model of the guitar string composed of a small set of point-masses joined by springs. This simple model can be used to demonstrate some of the properties found in actual guitar strings.

In the model I built with Interactive Physics, I am able to simulate plucking the string in different positions, and see how the overtone series of the string differs. If I "pluck" this simulated string in the middle section, the oscillation of the string will have a sinusoidal waveform. Plucking the string near one of its end points will cause the string to oscillate with a more complex overtone series, just as a guitar string plucked near the bridge will yield a more complex tone. It is so gratifying to build a mathematical-computational model and see that it agrees with the "real-world".

Below is a picture of this model of a guitar string, and a graph of the sinusoidal vibrations exhibited by the simplest mode of vibration of the model.